Color Encoding:
When video cameras or stills cameras are used to capture images from a scene, in many cases, the aim is that the resulting image reproduces colors on a display device that are as close as possible to the real colors in the scene. Therefore, the camera needs to be calibrated. To understand this problem of camera calibration, some background on color encoding and camera calibration is reminded below.
Each image generated by a camera consists of color signal values that are expressed as RGB color space coordinates in a color space which is device-dependent. These color coordinates are usually binary encoded. Such a color space depends on the type of the camera. Therefore, after having captured a scene, a camera represents colors of this scene by color coordinates. According to the terms of the ISO 22028-1, such a process of color representation is called scene-referred color encoding. See “Photography and graphic technology—Extended colour encodings for digital image storage, manipulation and interchange—Part 1”, in Architecture and requirements, ISO 22028-1. Scene referred color encoding identifies color coordinates that are meant to be directly related to radiometric or photometric entities of the real world. For example, the raw RGB output values of a digital camera are usually transformed to scene-referred R′G′B′ values, such as defined by the output-referred ITU-R BT.709 standard. Such a color transformation corresponds to a calibration of the camera since the standard ITU-R BT.709 specifies the relation between scene-referred R′G′B′ values and photometric scene values XYZ.
Output-referred color encodings are notably obtained by color matching experiments. An output-referred color space and the related color matching experiment are generally defined by:                the characteristics of the output device used to reproduce the colors of a scene, which is driven by the output-referred color coordinates, and        the characteristics of the observer that perceives the colors reproduced by this output device.        
Let us take as example the output-referred R′G′B′ coordinates being input to a display device. The related trichromatic colour matching experiment is classical and involves the CIE 1931 standard (human) observer, corresponding to the average behavior of a small group of test persons. In the experiment, an observer compares the color reproduced by the display device with the color of a monochromatic light of a specific wavelength. For each wavelength, the observer adjusts the R′G′B′ values such that both colors match. The result of a color matching experiment are three color matching functions (red, green and blue) indicating, for each wavelength, which R′G′B′ coordinates should be input to the display device in order to match the monochromatic light.
The classical color matching function results in the output-referred R′G′B′ color space of the specific RGB display device that was used at the time of the experiment. An RGB color space needs to be defined for any other RGB display device that may be used to reproduce the colors. That is why output-referred RGB color spaces are device-dependent, too.
Better known is the output-referred CIE 1931 XYZ color space based on an ideal display device, with XYZ input signals and mathematically derived XYZ primaries. CIE 1931 XYZ color space is device-independent. XYZ color coordinates encode a color according to these standardized primaries and according to the CIE 1931 standard observer.
Less known is that we could build an RCGCBC or XCYCZC output-referred color space that is based on a digital camera as observer. Let us recall that output-referred color spaces not only depend on the aimed display device but also on the referred camera used as observer.
Linear output-referred color spaces can be transformed into each other using a linear color transform as far as the same observer is considered. Hunt shows this for RGB-XYZ transform and the SPMTE shows this for different RGB spaces of different display devices. Trichromatic observers (such as the human eye or usual digital RGB cameras) are characterized by the spectral sensitivities of their three kinds of photoreceptors. The three corresponding sets of spectral sensitivities are directly linked to a set of three XYZ color matching functions. One set can be derived from the other but they are of different nature.
Camera Calibration:
New requirements in images production using digital cameras include the capture of scenes showing colors with wider color gamut. Directors start to light scenes on production sets with colors that are out of the color gamut of usually used proof viewing devices (such as Rec. 709 monitors). For example in music life events, modern spot lights use programmable color filters able to generate light of high degree of saturation out of the usual Rec. 709 color gamut. In traditional production using digital cameras, such colors are avoided. In straight forward signal processing, illegal RGB values may be simply dipped somewhere in the imaging chain. This causes the color output on the reference screen to be widely different from the colors that can be seen in the scene. There is a need of controlled handling of out-of-gamut colors, in which the errors are minimized.
Scene-referred color encoding is ambiguous due to sensitivity metamerism. A common camera transforms a real-world color stimulus, defined by a spectrum, into a set of three RGB color coordinates. Similarly to human eyes, cameras are subject to metamerism. This raises issues in two directions:                A given camera may produce an identical set of RGB color coordinates for two different spectral color stimuli, called a metameric pair,        A camera with sensitivity curves different from the human eye differs in their metameric pairs from a human observer.        
The link between scene-referred camera RGB values and CIE 1931 XYZ coordinates cannot be trivial since two different spectral sensitivity curves are involved, that of the camera and that of the human eye, respectively. Camera and human eye may differ in their metameric pairs leading to non-invertible relations between RGB and XYZ coordinates such as illustrated in FIG. 1. Distinct rg points can correspond to the same xy point and vice versa. rg and xy chromaticity coordinates are obtained from the RGB scene-referred camera output values and from the output-referred CIE 1931 XYZ values, respectively, by normalization, as explained in the book entitled “The reproduction of color”, from R.W.G. Hunt, Wiley, 2004, Sixth Edition.
This problem is referred to as sensitivity metamerism and can be avoided completely only if the camera satisfies the Luther condition, i.e. If its spectral sensitivities are linear combinations of the color matching functions of the CIE 1931 standard observer. Another possibility is multispectral cameras that reduce the effect of sensitivity metamerism: see the article entitled “Evaluating Wide Gamut Color Capture of Multispectral Cameras”, from Yuri Murakami, Keiko Iwase, Masahiro Yamaguchi, Nagaaki Ohyama, in Proceedings of 16th IS&T Color Imaging Conference, November 10-15, Portland, 2008.
If a given camera does not satisfy the Luther condition (such as most cameras) and if it is not multispectral but has just three color channels (such as most cameras), sensitivity metamerism cannot be avoided. In order to minimize the effects, sets of scene-referred color coordinates, for example sets of CIE 1931 XYZ values, need to be estimated from sets of raw RGB color coordinates directly outputted by the camera. This process is called in the following camera calibration.
One common way of camera calibration is to use a MacBeth Color Checker Chart. Given an illuminant, each color patch of this chart has a known set of XYZ color coordinates. The camera captures the chart. The set of raw RGB color coordinates obtained by the capture of the different color patches of the chart and the associated known set of XYZ values associated to these color patches are used in a linear regression model to find a linear scene analysis parametric color transform (a 3×3 matrix) that transforms sets of raw RGB values to corresponding sets of XYZ coordinates. Then, XYZ coordinates are transformed by a predetermined linear output color transform into output-referred R′G′B′ coordinates. This first color transform is the camera parametric transform that transforms raw RGB values into standardized, scene-referred XYZ coordinates. The concatenation of the camera parametric transform with the output color transform gives a camera color calibration transform that transforms raw RGB values into output-referred R′G′B′ coordinates.
A draft technical report from ISO proposes two preferential methods to calculate such a calibration color transform: see ISO TC 42 N 574, 2010-05-18, ISO/DTR 17321-2, ISO TC 42/WG 20, Graphic technology and photography—Colour characterization of digital still cameras (DSCs)—Part 2: Considerations for determining scene analysis transforms.
The first method is called in the report “Scene analysis transform determined using a test target” and corresponds to the already described method. The second method is called in the report “Scene analysis transform determined using spectral measurements” and is similar to the first method but instead of a test target, explicit training spectra are exposed to the camera.
The ISO report explains that—for the first method—it is preferable to choose “test patches that simulate the spectral radiances of real-world colours of interest. The report further explains that—for the second method—it is preferable to choose “training spectra that simulate the spectral radiances of real-world colours of interest”.